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  • Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm times 8 cm times 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid.

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm \times 8 cm \times 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use\; \pi =3.14]

Answers (1)

Answer: 488

We know that, Volume of a  sphere is given as : \frac{4}{3}\pi r^{3}          (where r is the radius)

Given that radius of each sphere \left ( r \right )=2\; cm

So, Volume of sphere=\frac{4}{3}\pi r^{3}

                                   =\frac{4}{3}\times \pi \times \left ( 2 \right )^{3}

                                   =\frac{32}{3}\times 3.14

Volume of 16 spheres =16\times \frac{32}{3}\times3.14

                                    =535.89\; cm^{3}

Internal dimensions of given rectangular box =16 \times 8 \times 8\; cm

The box is in the form of a cuboid.

Volume of rectangular box =l \times b \times h

                                           =16\; cm \times 8\; cm \times 8\; cm

                                           =1024\; cm^{3}

Now it is given that when 16 spheres are packed, the box is filled with preservative liquid. So,

The total volume of rectangular box = Volume of 16 spheres - Volume of preservative liquid

The volume of preservative liquid =\left ( 1024-535.89 \right )cm^{3}

                                                =488.11\; cm^{3}

Thus, the volume of preservative liquid is 488.11\; cm^{3}

                                    

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